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The ability to grab, hold, and manipulate objects is a vital and fundamental operation in biological and engineering systems. Here, we present a soft gripper using a simple material system that enables precise and rapid grasping, and can be miniaturized, modularized, and remotely actuated. This soft gripper is based on kirigami shells—thin, elastic shells patterned with an array of cuts. The kirigami cut pattern is determined by evaluating the shell’s mechanics and geometry, using a combination of experiments, finite element simulations, and theoretical modeling, which enables the gripper design to be both scalable and material independent. We demonstrate that the kirigami shell gripper can be readily integrated with an existing robotic platform or remotely actuated using a magnetic field. The kirigami cut pattern results in a simple unit cell that can be connected together in series, and again in parallel, to create kirigami gripper arrays capable of simultaneously grasping multiple delicate and slippery objects. These soft and lightweight grippers will have applications in robotics, haptics, and biomedical device design.